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Question

Find the domains of definition of the following function:
y=15x7x7

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Solution

case1
15x05x1x15
and
7x7>0
7x>7
7x1>1
taking log we get
(x1)log7(7)>log7(1)
(x1)>0
x+1<0
so, x<(1)

case2
15x05x1x15
and
7x7<0
7x<7
7x1<1
taking log we get
(x1)log7(7)<log7(1)
(x1)<0
x+1>0
x>(1)
so x15
thus combiningly, domain is
f(x)=(,1)(15,)




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